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Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/...

Define a sequence (xn)n≥1 recursively by x1 = 1, x2 = 2, and xn = ((xn−1)+(xn−2))/ 2 for n > 2. Prove that limn→∞ xn = x exists and find its value.

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